Texture will not appear on the mesh
I downloaded your file, and though the applied material seems to have a reddish color in the material slot, the base color is light grey which is also what is appearing in the viewport views. When I changed it, the color of the model changed as well. Since the UV unwrap looks fine, I went one further and used nodes to add a checker texture just to test and it works fine. See below:

As you can see, the texturing seems fine. Is there something else i'm missing that is not working for you?